x^2=1.25(1.5^2-3x+x^2)

Solution for x^2=1.25(1.5^2-3x+x^2) equation:

x^2=1.25(1.5^2-3x+x^2)

We move all terms to the left:

x^2-(1.25(1.5^2-3x+x^2))=0


We calculate terms in parentheses: -(1.25(1.5^2-3x+x^2)), so:

1.25(1.5^2-3x+x^2)

We multiply parentheses

1.25x^2-3.75x+2.8125

Back to the equation:

-(1.25x^2-3.75x+2.8125)


We get rid of parentheses

x^2-1.25x^2+3.75x-2.8125=0

We add all the numbers together, and all the variables

-0.25x^2+3.75x-2.8125=0

a = -0.25; b = 3.75; c = -2.8125;
Δ = b2-4ac
Δ = 3.752-4·(-0.25)·(-2.8125)
Δ = 11.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3.75)-\sqrt{11.25}}{2*-0.25}=\frac{-3.75-\sqrt{11.25}}{-0.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.75)+\sqrt{11.25}}{2*-0.25}=\frac{-3.75+\sqrt{11.25}}{-0.5}
$